See zootzoot , zootzootplex , zootzootzootplex , etc.
Wait, what even is this?[]
Basically, I figured out a way to extrapolate on the zootzoot, zootzootplex, etc.
zootzoot = googol!1
zootzootplex = googolplex!1
zootzootduplex = googolduplex!1
etc.
On the page where the numbers besides zootzootplex are named, Username95387 names up to zootzootdeciplex, and then:
zootzootzootplex = zootzootplex!1
That data can give the impression that:
zootzoot-x-plex = googol-x-plex!1
zootzootzoot-x-plex = zootzoot-x-plex!1
Which, in turn, can lead to:
zootzootzootzoot-x-plex = zootzootzoot-x-plex!1
zootzootzootzootzoot-x-plex = zootzootzootzoot-x-plex!1
...
(n "zoot"s)-x-plex = (n-1 "zoot"s)-x-plex!1
which can lead to a long series of extrapolation from the zootzootplex and its analogies.
I've recently thought of a way to denote these, creating kind of a series.
The Notation[]
So, here's what I've come up with:
Z(a,b) = (b "zoot"s)-a-plex
That means that:
zootzoot = Z(0,2)
zootzootplex = Z(1,2)
zootzootduplex = Z(2,2)
zootzootzootplex = Z(1,3)
and, in turn, many numbers can be coined beyond this.
For a technical definition of how the function works without mention of extrapolation:
Z(n,1) = E100#(n+1)
Z(n,x) = (Z(n,x-1))!1
Extension into higher-order googols[]
Yes, we can extend this into further means.
Let's say that:
Z(0,1,2) = 10↑↑100 (giggol )
Z(n,1,2) = 10↑↑(Z(n-1,1,2) (giggol-n-plex)
Z(n,x,2) = (Z(n,x-1,2)!2 (because !1 would be too weak on a pentational scale)
By means of name extrapolation:
Z(0,2,2) = zittzitt (analogous to "giggol")
Z(1,2,2) = zittzittplex
Z(2,2,2) = zittzittduplex
...
Z(0,3,2) = zittzittzitt
Z(1,3,2) = zittzittzittplex
etc.
Go one step further, to say:
Z(0,1,3) = 10↑↑↑100 (gaggol )
Z(n,1,3) = 10↑↑↑(Z(n-1,1,3) (gaggol-n-plex)
Z(n,x,3) = (Z(n,x-1,3)!3 (because !2 would be too weak on a hexational scale)
So, again with extrapolation:
Z(0,2,3) = zattzatt (analogous to "gaggol")
Z(1,2,3) = zattzattplex
Z(2,2,3) = zattzattduplex
...
Z(0,3,3) = zattzattzatt
Z(1,3,3) = zattzattzattplex
etc.
Continue this, such that...
Z(0,1,y) = 10{y}100
Z(n,1,y) = 10{y}(Z(n-1,1,y) (gaggol-n-plex)
Z(n,x,y) = (Z(n,x-1,y)!y (where y still indicates a hyperfactorial)
Continue to say:
Z(0,2,4) = zeetzeet (analogous to "geegol")
Z(1,2,4) = zeetzeetplex
Z(0,3,4) = zeetzeetzeet
Z(0,2,5) = zitzit (analogous to "gigol")
Z(1,2,5) = zitzitplex
Z(0,3,5) = zitzitzit
Z(0,2,6) = zottzott (analogous to "goggol")
Z(1,2,6) = zottzottplex
Z(0,3,6) = zottzottzott
Z(0,2,7) = zatzat (analogous to "gagol")
Z(1,2,7) = zatzatplex
Z(0,3,7) = zatzatzat
Can we go further using the notation? Absolutely! But Bowers hasn't developed names for the primitive googol series beyond gagol, so we cannot name anything further than the zatzat series.
Maybe Z(n,x,100) can coin us the wootwoot series, analogous to the woogol ? I don't know.
I don't know what I could do for, say, a 4th entry or beyond, so I'll just leave it at this for now.